Exponential Attractors in Generalized Relativistic Billiards

Coding of billiards in hyperbolic 3-space

“…While the problem in 2-dimensions is well supplemented by the geometric intuition one gets from the two dimensional models of the hyperbolic plane, the case of higher dimensions is devoid of anything of that sort. Due to this, the work in 3-dimensions and higher is limited to the problem involving relativistic billiards that has been dealt in [4,5,6,15].…”

Computational study of the dynamics of an asymmetric wedge billiard

“…Research has also been done on modifications of classical billiard systems. It would be natural to consider the particle moving in the quantum realm [7,37,39] or moving relativistically [11,12,13]. Other billiard systems consider modifications to the region of motion itself, for example, a hole or multiple holes within the region-these are the so-called "open billiards"; billiard systems where the boundary changes in time [18,19,21,24,25,26]; and billiard systems where the billiard moves under the influence of a constant force field, either magnetic [3,10,14,30,38] or gravitational [9,20,23].…”

Ballistic electron transport in graphene nanodevices and billiards

“…1(d), which shows the "mushroom" billiard. Billiards are relevant in theoretical studies and modeling of nanodevices and have been used extensively to model nanodevices both from a classical [38,36,39,40,41,42,43,44,45,46] as well as quantum perspective [47,48,49,50], and have also been implemented extensively specifically for graphene [51,46,52,53].…”

“…This provides an intuitive framework for one to conceptualize what mean return times mean (which is what Kac's lemma provides). Fourthly, billiards have been used extensively in many areas of physics, like ergodic theory [110,119,120], quantum chaos [47,48], optical microresonators and laserss [49,50] and room acoustics [121]) and also in condensed matter to model transport properties of electronic nanostructures such as quantum dots and antidot superlattices [122,36,97,40,41,42,43,44,45,46] and even more specifically for graphene nanodevices [51,46,52,53]. This means that any general results we can find about billiards could have potential implications for various areas of physics and thus have a broad impact.…”